# Optimal General Factor Problem and Jump System Intersection

@inproceedings{Kobayashi2022OptimalGF, title={Optimal General Factor Problem and Jump System Intersection}, author={Yusuke Kobayashi}, booktitle={Conference on Integer Programming and Combinatorial Optimization}, year={2022} }

In the optimal general factor problem, given a graph $G=(V, E)$ and a set $B(v) \subseteq \mathbb Z$ of integers for each $v \in V$, we seek for an edge subset $F$ of maximum cardinality subject to $d_F(v) \in B(v)$ for $v \in V$, where $d_F(v)$ denotes the number of edges in $F$ incident to $v$. A recent crucial work by Dudycz and Paluch shows that this problem can be solved in polynomial time if each $B(v)$ has no gap of length more than one. While their algorithm is very simple, its…

## One Citation

### Jump-systems of $T$-paths

- Mathematics
- 2023

Jump systems are sets of integer vectors satisfying a simple axiom, generalizing matroids, also delta-matroids, and well-kown combinatorial examples such as degree sequences of subgraphs of a graph.…

## 31 References

### Optimal General Matchings

- MathematicsWG
- 2018

This paper considers a version of the general matching problem, in which it is interested in finding a B-matching having a maximum (or minimum) number of edges.

### M-Convex Functions on Jump Systems: A General Framework for Minsquare Graph Factor Problem

- MathematicsSIAM J. Discret. Math.
- 2006

A local optimality criterion is given for minimization of an M-convex function subject to a component sum constraint on the degree sequences of an undirected graph.

### TIME BOUNDS OF BASIC STEEPEST DESCENT ALGORITHMS FOR M-CONVEX FUNCTION MINIMIZATION AND RELATED PROBLEMS

- MathematicsJournal of the Operations Research Society of Japan
- 2021

Norito Minamikawa, Akiyoshi Shioura (Tokyo Institute of Technology) The concept of M-convex function gives a unified framework for discrete optimization problems with nonlinear objective functions…

### Complexity of Matroid Property Algorithms

- Mathematics, Computer ScienceSIAM J. Comput.
- 1982

A general theorem is proved which can be used to show that for a large number of matroid properties there is no good algorithm of a certain type for determining whether these properties hold for…

### General Antifactors of Graphs

- MathematicsJ. Comb. Theory, Ser. B
- 1993

A "Tutte-type good characterization" (and a simple polynomial algorithm) is given to decide this question when several unlucky numbers are allowed.